This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ) , w ( · ) = ( v ( · )) . Make sure that your conditions are satisﬁed at least for one nonzero transfer function G = G ( s ). Problem 4.3 For the pendulum equation y ¨( t ) + ˙ y + sin ( y ) = , ﬁnd a single continuously diﬀerentiable Lyapunov function V = V ( y, y ˙) that yields the maximal region of attraction of the equilibrium y = y ˙ = 0. (In other words, the level set x ² R 2 : V (¯ { ¯ x ) < 1 } schould be a union of disjoint open sets, one of which is the attractor ± of the zero equilibrium, and V ( y ( t ) , y ˙( t )) schould have negative derivative at all points of ± except the origin.)...
View
Full Document
 Spring '09
 AlexandreMegretski
 Dynamics, LTI system theory, Linear system, Nonlinear system

Click to edit the document details